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Questions  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Q)

Integrate: $\int (2x-7) \sqrt {5x+2} dx$

$(a)\;\frac{4}{5}(5x+2)^{3/2}-26 (5x+2)^{5/2}+c \\(b)\; \frac{4}{5}(5x+2)^{5/2}-26 (5x+2)^{3/2}+c \\(c)\; 26 (5x+2)^{3/2}-\frac{4}{5}(5x+2)^{5/2} +c \\ (d)\;None$

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A)
$2 \int (x-\large\frac{7}{2} )$$ \sqrt {5x+2}dx$
=> $10 \int (5x-\large\frac{35}{2} )$$\sqrt {5x+2}dx$
=> $10 \int \{(5x+2)- (\large\frac{35}{2}$$+2)\} \sqrt {5x+2}$$dx$
=> $10 \int (5x+2)^{3/2} dx-10 \int \large\frac{39}{2}$$. \sqrt {5x+2}$$dx$
=> $\large\frac{1}{5} $$ \times 10 \times \frac{2}{5} (5x+2)^{5/2} -\large\frac{390}{2} \times \frac{2}{3} \times \frac{1}{5}$$ \sqrt {(5x+2)^{3/2}}+c$
=>$\large \frac{4}{5}$$(5x+2)^{5/2}-26 (5x+2)^{3/2}+c$
Hence b is the correct answer.
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